Probability

Question

 The attendees of a technology oriented conference come from either northern Indiana or southern Indiana. You are told that there are twice as many attendees from southern Indiana as there are from northern Indiana. Further, 10% of the southern Indiana attendees are engineers. On the other hand, 15% of the northern Indiana attendees are engineers. What's the probability of being an engineer at this conference? 

Answer 1

Let N = number of attendees from northern Indiana

Then 2*N = number of attendees from southern Indiana

 

Note there are 3*N total attendees

 

10% of southern Indiana attendees are engineers  ==>  

0.10*(2*N) = 0.2*N engineers from southern Indiana

 

15% of northern Indiana attendees are engineers ==> 

0.15*N engineers from northern Indiana

 

Total number of engineers = 0.2*N + 0.15*N = 0.35*N

 

Probability of being an engineer at this conference is 

0.35*N / (3*N) = 35/300 = 7/60 ~ 0.1167 = 11.67% 

 

Answer 2

Draw a diagram, here is one:

 

http://hwmath.net/solutions/IndianaConference.jpg

 

Check the answer by finding the probability of being an engineer at this conference, and the probability of being something other than an engineer at the conference.